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C₂³×C₅²×C₁₉ #72183377

order	3800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1451520
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅

Aliases

abelian	C₂³×C₅²×C₁₉
multiplicative	(ℤ/6303)ˣ, (ℤ/8404)ˣ, (ℤ/12606)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

256 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₅²×C₁₉, C₂⁴×C₅²×C₁₉, C₂³×C₃×C₅²×C₁₉, …
maximal normal subgroup of	C₂²×C₄×C₅²×C₁₉, C₂⁴×C₅²×C₁₉, C₂³×C₃×C₅²×C₁₉, …
maximal quotient of	C₂²×C₄×C₅²×C₁₉, C₂⁴×C₅²×C₁₉, C₂³×C₃×C₅²×C₁₉, …
automorphism group of	C₃×C₁₁×C₁₉₁, C₄×C₁₁×C₁₉₁
outer automorphism group of	C₃×C₁₁×C₁₉₁, C₄×C₁₁×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.